Open AccessAnalysis of fractional hybrid differential equations with impulses in partially ordered Banach algebras
Author(s) -
Jin You,
Zhenlai Han
Publication year - 2021
Publication title -
nonlinear analysis
Language(s) - English
Resource type - Journals
eISSN - 2335-8963
pISSN - 1392-5113
DOI - 10.15388/namc.2021.26.24939
Subject(s) - mathematics , nonlinear system , quadratic equation , differential equation , perturbation (astronomy) , class (philosophy) , fixed point theorem , banach space , mathematical analysis , computer science , physics , quantum mechanics , geometry , artificial intelligence
In this paper, we investigate a class of fractional hybrid differential equations with impulses, which can be seen as nonlinear differential equations with a quadratic perturbation of second type and a linear perturbation in partially ordered Banach algebras. We deduce the existence and approximation of a mild solution for the initial value problems of this system by applying Dhage iteration principles and related hybrid fixed point theorems. Compared with previous works, we generalize the results to fractional order and extend some existing conclusions for the first time. Meantime, we take into consideration the effect of impulses. Our results indicate the influence of fractional order for nonlinear hybrid differential equations and improve some known results, which have wider applications as well. A numerical example is included to illustrate the effectiveness of the proposed results.